Differential games described by infinite system of differential equations

Different approaches have been used by many researchers to solve control problems for parabolic and hyperbolic partial differential equations. Some of these problems can be reduced to the ones described by infinite systems of ordinary differential equations by using the decomposition method. Therefore there is a significant relationship between control problems described by partial differential equations and those described by infinite system of differential equations. We study three types of infinite systems. The first is infinite systems of first order differential equations. The second system is infinite system of second order differential equations and the third system is infinite system of 2-systems of first order differential equations. In this thesis, we study the uniqueness and existence theorems for all systems then we study control and differential game problems. For the first system, we study a pursuit game of one pursuer and one evader and evasion differential game of one evader from infinitely many pursuers in the case of integral constraints. For the second system, we study an evasion differential game of one evader from finite number of pursuers in the case of geometric constraints and for the third system, we study a control problem.

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